Abstract

The computer industry has seen an immense development in the last decades. Personal computers have become available for everybody living in industrialized countries with rapidly increasing performance in terms of speed and storage capacities. However, the performance of nowadays' computers is fundamentally limited by the laws of classical physics: a classical bit can only take on either of the two distinct values `0' or `1'. In contrast, a quantum computer could, in principle, make direct use of quantum phenomena, such as state superpositions -- a quantum bit can be in both states `0' and `1' simultaneously --, to perform complex computational tasks much faster than any classical computer. The idea of building computers that work according to the laws of quantum physics has opened various fields of research, one of which is the search for the best physical system to use as a quantum bit (qubit). One important criterion for determining the optimal qubit system is the lifetime of state superpositions. Typically, once initialized, such superpositions are destroyed on remarkably short timescales due to interactions with the environment -- a process which is referred to as decoherence --, posing the question which physical qubit candidate system might show a high-enough robustness against the influence of the `outside world' to allow for viable quantum computation. In this thesis, we will consider three particular realizations of one specific and very promising type of qubit candidate system: an electron (or hole) confined to a quantum dot -- a nanoscale structure within a (typically semiconducting) material --, where the spin states `down' and `up' of our electron (or hole) encode the logical states `0' and `1'. Our task will be to study the decay of spin-state superpositions in such quantum-dot systems. The main objective of this thesis is to understand the most important physical processes that lead to spin decoherence and to show ways to suppress this undesirable effect. It turns out that at low temperatures, the main source of decoherence is the coupling of the electron (hole) to the surrounding nuclear spins. This thesis is divided into three logical parts, corresponding to the three qubit candidate systems under consideration. First we will study electron-spin qubits in III-V semiconductor quantum dots, where the electron spin interacts with the nuclear spins of the semiconducting host material via the isotropic Fermi contact hyperfine interaction. Second we consider quantum-dot-confined heavy holes and the decoherence of their (pseudo-)spin states due to anisotropic interactions with the nuclear spins. Third and last, we study electron-spin qubits made from carbon-nanotube and graphene quantum dots. Quantum dots made of carbon have the advantage of a low abundance of spin-carrying nuclear isotopes, therefore reducing decoherence effects significantly. For each of the systems under consideration, we will carry out analytical calculations on the nuclear-spin interactions and the spin dynamics of the qubit. Although one main goal of this thesis is to show ways to extend spin decoherence times, we will also focus on physically more fundamental questions. Not only the timescale of the decay is relevant for the system's applicability as a qubit, but also the form of the decay which can vary significantly from system to system. For example, the decay of spin-state superpositions can follow an exponential, super-exponential or power-law decay, and can even pass through various stages. This is not only of academic interest, but also important for practical purposes, such as the implementation of quantum error-correction schemes in a potential quantum computer.